Chevalley Supergroups of type D(2,1;a)

Abstract

I present a construction "a` la Chevalley" of affine supergroups associated with simple Lie superalgebras of (classical) type D(2,1;a), for any possible value of the parameter a - in particular, including non-integral values of a. This extends the similar work performed in [R. Fioresi, F. Gavarini, "Chevalley Supergroups", Memoirs of the AMS 215 (2012), no. 1014 - arXiv:0808.0785v8 [math.RA]], where all other simple Lie superalgebras of classical type were considered. The case of simple Lie superalgebras of Cartan type is dealt with in [F. Gavarini, "Algebraic supergroups of Cartan type", Forum Mathematicum (to appear), 92 pages - arXiv:1109.0626v5 [math.RA], so this work completes the program of constructing connected affine supergroups associated with any simple Lie superalgebra.

La-TeX file, 20 pages. All the text was amended after the referee's remarks. To appear in "Proceedings of the Edinburgh Mathematical Society"

References in corpus (2)

• A new proof of the Mullineux conjecture
• Modular representations of the ortho-symplectic supergroups

Cited by in corpus (3)

• Chevalley Supergroups
• Minimal W-superalgebras and modular representations of basic Lie superalgebras
• Algebraic supergroups and Harish-Chandra pairs over a commutative ring